craftgrrl | Knitted Houndstooth Shawl Shedding

I didn't see anything about this in the rules but I tried asking my domestic communities to no avail. Mods feel free to delete.

I went to a Civil War Reinactment last year and my boyfriend bought me a knitted houndstooth shawl that I LOOOOVEEEE. But it sheds like CRAZY. Its a very soft thin yarn that was used, but I have little to no experience with yarn besides latch hooking when I was a kid. I have only worn the shawl twice and never washed it. The seller was not the creator so he didn't know anything about fiber content.

Is there a way to keep my shawl from shedding since it looks especially good with black clothing?

I googled and found that my options are to just deal with it, spray it down with hairspray, or wash it with conditioner (although I don't think this is real hair yarn so not sure about that one).

Has anyone had any experience with this? Any magic laundering ideas that frequent knitters use?